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Women and members of certain ethnic groups take the biggest hit, said Katrina Piatek-Jimenez, a faculty member in CMU's mathematics department.

The result for society as a whole: a big minus sign.

"By certain individuals not being part of the field we are losing great minds," said Piatek-Jimenez, who for years has researched reasons why people pick — or don't pick — mathematics as a field of study.

Clichés about mathematicians are everywhere: TV, movies, on the internet and in school hallways.

In fact, middle school is where the parting of the ways often begins.

For many small children, math is fun. To them, crunching a complicated story problem is like solving a tough puzzle. It's a game.

But numerous studies show girls start checking out around middle school, Piatek-Jimenez said, especially those who place a greater focus on looks, clothing and fitting in.

"The stereotypes of a mathematician are that they're obsessed with mathematics and don't care about their personal hygiene," she said. "They don't care about their personal lives. Maybe they don't have a lot of friends. They're loners."

Most kids — boys and girls — don't want to fit that image.

"I think that also it's seen as not popular or cool to be really smart in middle school," she added, "and mathematicians are seen as being really smart."

Perceived intelligence is a stereotype that actually can encourage certain other minorities. Asians and people from the Middle East and India are seen as being naturals at mathematics and are more likely to stick with it, Piatek-Jimenez said.

And yet the same stereotype also implies other groups — such as African Americans, Hispanics and Native Americans — can't hack the subject. They're the most likely to shy away, she said.

"The research shows that there's no biological gene of being good at math, and it has certainly no ties to gender or ethnicity," she said, "but unfortunately there are still a lot of people who have these biases."

Find the mathematicians

The stereotypes also interest Miranda Nouhan and Michaela Williams, future elementary school teachers who expect to graduate from CMU in December and whose research Piatek-Jimenez oversaw last year.

In their study, 179 CMU students were asked to describe mathematicians in words and pictures.

Some version of "smart" was the most frequent descriptor, she said, while teacher and professor appeared most often as possible math careers.

In another exercise, a dozen student focus group volunteers were shown photos of eight men and eight women of various ages. Half of the photos were of actual mathematicians — four women and four men.

The stereotypes were played up a bit. There was an Asian man, an Asian woman, an Indian man and a black woman. The Indian man was playing the drums. A woman with dreadlocks was shown camping.

The camping woman, for example, was a mathematician.

"People very rarely thought that," Piatek-Jimenez said. "They often said, 'She looks too carefree to be a mathematician,' or 'She's camping, so maybe she's a biologist.'"

The Indian drummer also was a mathematician. In fact, he was a recipient of the Fields Medal, an award she described as "the Nobel Prize of mathematics."

Only three of the 12 students got that one right, Piatek-Jimenez said.

"Another stereotype is that mathematicians don't have any hobbies outside mathematics. All they do all day is mathematics," she said. "We definitely saw that coming through in the focus groups."

Another photo showed a man with glasses, facial hair and a disheveled look. Most students pegged him as a math guy.

He was a dance professor.

Then there was a picture of Danica McKellar, an actress perhaps best known from the TV show "The Wonder Years."

She's not only a mathematician whose name is included in the title of a mathematical theorem, she's also the author of books on math aimed at middle-school girls.

Several students missed that one, too.

In October, Nouhan, Williams and Piatek-Jimenez will present their work to the North American chapter of the International Group for the Psychology of Mathematics Education in Indianapolis.

Pervasive problem

Television shows such as "The Bang Theory" and films such as "Revenge of the Nerds" bolster the stereotypes, Piatek-Jimenez said. Sometimes the news media do, as well.

Consider coverage of the Fields Medal winners.

"When the journalists write up stories about these people, they often focus on their obsession with mathematics," she said.

"It makes a good story about how you spent seven years working on this mathematical problem, but it also reinforces these stereotypes."

"I think we're missing out on a lot of different advances that we would be able to make otherwise in a more diverse workforce," she said.

Then there's the money. Many math-related jobs pay well, and backing away from the field costs women and certain minorities a shot at higher salaries for themselves and a chance to tighten the wage gap between themselves and white men.

"I think it's a shame that certain minorities and women are less likely to go into these lucrative careers partially as a result of the stereotypes," she said.

What to do?

The obvious solution, Piatek-Jimenez said, is to get more women and minorities into mathematics. But how?

One mission is to educate teachers, although there's no quick fix. At CMU, Piatek-Jimenez and math faculty colleague Donna Ericksen developed an elective course called "Mathematics and Popular Culture." First offered to students in 2008, the class addresses math stereotypes.

Elementary education students are encouraged to take it.

"We need teachers who motivate the girls as well as the boys, and who give them the challenging problems and the challenging questions, as well," she said.

There also is the rising number of STEM camps. Girls on the fence about math can find a sanctuary where they don't feel alone, Piatek-Jimenez said. CMU, for example, has no shortage of STEM summer camps.